Free Descriptive Statistics MCQs with Answers

• A. Given value
• B. All +ve, -Ve value
• C. Zero reject
• D. None of these

Explanation: For n observations, the geometric mean is the nth root of their product, written as (x₁x₂⋯xₙ)^(1/n).

• A. Change
• B. Capable
• C. Understand
• D. Clear

Explanation: An average is useful only when its value and meaning can be understood readily by the people using it.

• A. 6
• B. 4
• C. 14/3
• D. 8

Explanation: The geometric mean is the cube root of the product: (2 × 4 × 8)^(1/3) = 64^(1/3) = 4. Therefore, option b is correct.

• A. Unassigned
• B. Arranged
• C. Continuous
• D. Discrete

Explanation: The median is the middle position only after the observations have been arranged in ascending or descending order.

• A. Zero
• B. Negative
• C. Positive
• D. All sign

Explanation: The harmonic mean uses reciprocals, as in n divided by the sum of 1/x values.

• A. Great
• B. lesser
• C. Equal
• D. None of these

Explanation: In a positively skewed distribution, the long right tail pulls the mean above the median. Hence the median is lesser than the mean.

• A. a+b/2
• B. 2ab/a+b
• C. √ab
• D. None of these

Explanation: For two values, the harmonic mean is obtained by dividing twice their product by their sum: 2ab/(a+b).

• A. Mean
• B. Median
• C. Harmonic
• D. Mode

Explanation: The sum of absolute deviations is least when deviations are measured from the median.

• A. Mean
• B. Median
• C. Mode
• D. G.M.

Explanation: The median depends on the middle position, so the observations must first be arranged in ascending or descending order.

• A. 4
• B. 6
• C. 8
• D. 30

Explanation: The mode is the value occurring most frequently. Here, 6 appears three times, more often than any other value.

• A. Median
• B. Combined mean
• C. A.M.
• D. None of these

Explanation: The coded or assumed-mean method simplifies calculation of the arithmetic mean by replacing observations with deviations from a chosen…

• A. A.M.
• B. Medain
• C. Mode
• D. H.M.

Explanation: The harmonic mean uses reciprocals, and a zero observation has a reciprocal that is undefined.

• A. Mode = 3 median - 2 mean
• B. Mode = 2 median -3 mean
• C. Median = 2 median-3 mean
• D. Mean- mode

Explanation: For a moderately skewed distribution, Pearson’s empirical relation is Mean − Mode ≈ 3(Mean − Median), which rearranges to Mode ≈ 3 Median…

• A. P33
• B. D3
• C. Median
• D. None of these

Explanation: The third quartile is the 75th percentile, written as Q3 = P75. Since P75 is not listed, none of these is correct.

• A. Stable
• B. manipulation
• C. Change
• D. Group

Explanation: The arithmetic mean is relatively stable because it uses every observation and generally varies less from sample to sample than the mode.

• A. Mean
• B. Sum
• C. Average
• D. 2.D.

Explanation: The algebraic sum of deviations from the arithmetic mean is always zero: Σ(x − x̄) = 0.

• A. G.M.
• B. Median
• C. Mean
• D. Harmonic mean

Explanation: Reducing the smallest observation keeps it at the lower end of the ordered data, so the middle position and hence the median remain…

• A. Arbitrary value
• B. Mean
• C. Mode
• D. G.M.

Explanation: The sum of squared deviations is minimized when deviations are measured from the arithmetic mean, a fundamental property of the mean.

• A. Mean
• B. Mode
• C. Median
• D. H.M.

Explanation: The mode is the value or category occurring with the highest frequency in a data set.

• A. Decease
• B. Smaller
• C. Largest
• D. Increase

Explanation: Adding a constant to every observation adds the same constant to the arithmetic mean: mean(new data) = mean(old data) + 10.